Frame-theoretic analysis of oversampled filter banks


Helmut Bölcskei, Franz Hlawatsch, and Hans G. Feichtinger


IEEE Trans. Signal Processing, Vol. 46, No. 12, pp. 3256-3268, Dec. 1998.

DOI: 10.1109/78.735301

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We provide a frame-theoretic analysis of oversampled, FIR and IIR, uniform filter banks (FBs). Our analysis is based on a new relation between the FB's polyphase matrices and the frame operator corresponding to a FB. For a given oversampled analysis FB, we present a parameterization of all synthesis FBs providing perfect reconstruction. We find necessary and sufficient conditions for an oversampled FB to provide a frame expansion. A new frame-theoretic procedure for the design of paraunitary FBs from given nonparaunitary FBs is formulated. We show that the frame bounds of a FB can be obtained by an eigenanalysis of the polyphase matrices. The relevance of the frame bounds as a characterization of important numerical properties of a FB is assessed by means of a stochastic sensitivity analysis. We consider special cases in which the calculation of the frame bounds and synthesis filters is simplified. Finally, simulation results are presented.


Oversampled FIR and IIR filter banks, frame theory, matrix representation, noise reduction


Received the 2001 IEEE Signal Processing Society Young Author Best Paper Award.

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